Abstract
Inspired by the cooking videos of the format “$n$ levels of [dish]”, I’m here applying a similar concept to scientific modeling. I will be comparing 4 levels of projectile motion, from the easiest “textbook” model, which is the simplest of all and assumes only constant gravity in a flat Earth, to a more complex model taking into account factors like quadratic drag, buoyancy, and the Magnus effect.
Level 1: just constant gravity in a vacuum
This is the easiest level of all. It is ubiquitous in all middle and high school level textbooks on physics (Serway & Jewett, 2016), and it’s commonly used as a way to teach the basic idea of 2D kinematics, and tracking the position as a function of time of an object in the $\mathbb{R}^{2}$ plane using parametric equations of the form $x = f(t)$, $y = g(t)$. Considering gravity in the negative $y$ direction to be the only force acting on the object, and, as Galileo noticed, if gravity is the only force on an object, the mass is not involved in the motion. We assume the object is significantly close to Earth’s surface, in which case constant gravity in a single direction can be assumed. With all of this information, Newton’s second law gives the simple equations